(i)[3]
A line is given by $y = 2x + c$ and a curve by $y = 8 - 2x - x^2$. When the line is tangent to the curve, determine the constant $c$.
(ii)[7]
When $c = 11$, determine the $x$-coordinates where the line and the curve meet. Also find, using integration, the area of the region enclosed by the line and the curve.